[tex]y= p+q\sqrt{2}[/tex] is a general element of [tex]\mathbb{Q}(\sqrt{2})[/tex] where p and q are rational. First you will need to show that if y is a solution to a polynomial over Z, then it is a solution to a polynomial over Z of degree 2. Then find necessary and sufficient conditions for y such that y is the solution of such a polynomial (use the fact that p and q are rational).
